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Andrew Odlyzko and Benjamin Tilly of the Digital Technology Center at the University of Minnesota have published an assessment of the value of networks that makes more modest claims than the so-called "Metcalfe's Law," which states that the value of a network increases with the square of the number of nodes.
They suggest that, as a rough rule of thumb, the value of a network of n people is given by the formula nlog(n)
Metcalfe's Law has always been dubious, a bit of dotcom-bubble buzz. Indeed, its supposed formulator Bob Metcalfe, inventor of Ethernet and a genuine genius of the era, is innocent of its perpetration, as documented by Paul Kedrosky at Infectious Greed).
In reality, as pointed out by Metcalfe himself and many others, it depends on the assumption that all contacts are equally valued. Starting from that point, the law becomes a simple application of the formula describing the number of possible two-person interactions in a network of n persons, which is equal to n(n-1)/2. (i.e., In a 4-person network, there can be 6 different 2-way conversations; in 5-person network, there can be 10; in a 10-person network, there can be 45.)
However, the underlying assumption is ridiculous. From the viewpoint of any participant in a network, many if not most of the other participants are noise, not value. You profit from their presence because it allows the provider to spread its fixed costs over a broader base, which reduces your personal share. But as far as actual communication goes -- you want to interact with a limited subset of subscribers, and what you really need is a way to filter out most of the others so you can focus on this subset. (Viz., current controversies over spyware and spam, and the great challenge of designing search engines is not in finding references but in excluding them.)
Of course, this sour view also misses some things. It assumes that you know in advance with whom you wish to communicate. It does not capture the option value of being able to search out new sources of information; contemporary networks are not just glorified telephones but multi-directional broadcast media as well, which makes analysis of their value exceedingly difficult to conceptualize.
Nor does the skeptical view capture the value of group formation. A network of 3 people can have three different 2-person talks, but it can also have a 3-person conference call. A network of 4 can have 6 2-way conversations, but it also can have a 4-way interaction, as well 4 different 3-way groupings. A variation called Reed's Law took Metcalf's law a step further, concluding that the value goes up even faster, as a function of the number of possible groups.
Despite their detachment from reality, these laws have been a powerful paradigm, endorsed by, among others, Reed Hundt, former head of the FCC and generally regarded at PFF as one of the great destructive forces of the past decade. And, as C|Net said in its article on the new formula:
Metcalfe's Law was a driving feature of the dot-com boom. Netscape co-founder Marc Andreessen, for example, argued that the law explained the surging amount of time people spent online using services from America Online, his employer at the time. The authors point out that their rule of thumb (let's avoid "law") accounts for real world behavior of network participants more satisfactorily, concluding:
Metcalfe's Law and Reed's Law both significantly overstate the value of a communication network. In their place we propose another rough rule, that the value of a network of size n grows like n log(n). This rule, while not meant to be exact, does appear to be consistent with historical behavior of networks with regard to interconnection, and it captures the advantage that general connectivity offers over broadcast networks that deliver content. It also helps explain the failure of the dot-com and telecom ventures, since it implies network effects are not as strong as had been hoped for. They make a persuasive case, and certainly everyone interested in the Internet, telecom, and tech would profit from a more sober metric of potential value.
Bob Metcalfe should certainly be rooting for the success of the new formula. As Kedrosky notes, he has been and still is getting a bad rap for this, and would probably be delighted to have this non-accomplishment fade into oblivion.
posted by James DeLong @ 2:00 PM | Internet: P2P, Search Engines...
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